# Thermal Conductivity of Diamond at 300 Kelvin

I am tried to calculate the Thermal Conductivity of Diamond at 300 K.
But in journals, it saying that Diamond having very high values of Thermal conductivity and at 300K its about 2000W/(mK).

But in my calculation, i m getting the value of Thermal Conductivity less than 100 W/(mK)…

I am giving the detailed input script of my Calculation.
Can U give me any suggestion of this mismatching between Theory, Experiment & Simulation.

# Sample LAMMPS input script for thermal conductivity of Diamond

units metal
variable T equal 300
variable V equal vol
variable dt equal 0.001
variable p equal 100 # correlation length
variable s equal 10 # sample interval
variable d equal \$p*\$s # dump interval

# convert from LAMMPS metal units to SI

variable kB equal 1.3806504e-23
variable eV2J equal 1.602177e-19
variable A2m equal 1.0e-10
variable ps2s equal 1.0e-12
variable convert equal {eV2J}*{eV2J}/{ps2s}/{A2m}

# setup problem

dimension 3
boundary p p p
lattice diamond 3.5626 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
region box block 0 5 0 5 0 5
create_box 1 box
create_atoms 1 box
mass 1 12.0107
pair_style tersoff
pair_coeff * * SiC.tersoff C
timestep \${dt}
thermo \$d

# equilibration and thermalization

velocity all create \$T 102486 mom yes rot yes dist gaussian
fix NVT all nvt temp \$T \$T 10 drag 0.2
run 8000

# thermal conductivity calculation, switch to NVE if desired

#unfix NVT
#fix NVE all nve

reset_timestep 0
compute myKE all ke/atom
compute myPE all pe/atom
compute myStress all stress/atom virial
compute flux all heat/flux myKE myPE myStress
variable Jx equal c_flux[1]/vol
variable Jy equal c_flux[2]/vol
variable Jz equal c_flux[3]/vol
fix JJ all ave/correlate \$s \$p d & c_flux[1] c_flux[2] c_flux[3] type auto file J0Jt.dat ave running variable scale equal {convert}/\${kB}/\$T/\$T/\$V*s*
{dt}
variable k11 equal trap(f_JJ[3]){scale} variable k22 equal trap(f_JJ[4])*{scale}
variable k33 equal trap(f_JJ[5])
\${scale}
thermo_style custom step temp v_Jx v_Jy v_Jz v_k11 v_k22 v_k33
run 100000
variable k equal (v_k11+v_k22+v_k33)/3.0
variable ndens equal count(all)/vol
print “average conductivity: \$k[W/mK] @ T K, {ndens} /A^3”

Many Thanks & Kind Regards

Siby

There are many number of reasons.

But first i want to ask if the paper you are referring to has calculated the thermal conductivity by MD simulations, or by experiments, or by theory???

Sagar

I referred papers which contain purely theoretical calculations,

Experimental calculations and MD simulation also…

Even though all these values are little bit varying according to the method and parameters used. But all showing that diamond is a material which showing High Thermal Conductivity.

Response properties are in general not straightforward to compute and it could take many trial and error attempts to develop the expertise to handle such calculations. Gathering and looking at a bunch of papers is not enough (that, a librarian can do with no science degree but just a list of “matching keywords”). You need to apply the scientific method to your problem. Plain cut& paste from the examples directory won’t do it either. First, you need to identify a publication that has used EXACTLY the same forcefield you intend to apply via some MD simulations. If you can’t find it then switch your potential to one that has been tested in the lit (at least until you manage to learn the influence of all the other variables compromising the quality of your conductivity results). As your are trying to use the GK method you should be looking at understanding the shape of the correlation function and making sure that your sampling interval and correlation length do correspond to the morphology of the diamond one (were not taken from the Ar example). In solid systems, size effects could be the limiting step to computing properly the conductivity because of the phonon carriers. Ideally you would also want to use a secondary approach (any of the non-equilibrium techniques) to cross-validate your equilibrium calculations. The Lammps archives are another source of info and there have been past posts relating to your quest.
And so on…

Carlos

Nothng left to say for me, after Carlos’ comments.